Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations

TL;DR

This paper investigates how destructive agents called jokers induce stable cooperation-defection cycles in finite populations, demonstrating the robustness of these cycles across various selection rules through analytical and simulation methods.

Contribution

It provides the first analytical and simulation-based analysis of joker-driven cycles in finite populations, extending previous infinite population results.

Findings

Cycles occur in all studied cases, indicating robustness.

Joker dynamics induce persistent cooperation-defection cycles.

Average dominance times are computed and validated by simulations.

Abstract

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.